Active noise control systems using the well-known filtered-x LMS (least mean square) Algorithm are known for electrical noise cancellation. A general discussion is by S. Elliot and P. Nelson, Active Noise Control, IEEE Signal Processing Magazine, October 1993. The well-known filtered-x LMS Algorithm is discussed by B. Widrow and S. Stearns in a book, Adaptive Signal Processing, Prentice Hall, 1985. The above algorithm uses an adaptive filter in conjunction with a transfer function in the forward path which filters the input. The Filtered-x LMS algorithm is most ideally used in a single-input single-output (SISO) system. For multiple-input multiple-output (MIMO) systems, the Multiple Error LMS algorithm is a generalization of the Filtered-x LMS algorithm.
For the SISO system, the computational complexity is of a desirable order N, where N is the number adjustable parameters of the adaptive filter. However, in the multiple error LMS algorithm the desirable order N computational complexity of LMS is lost, resulting in prohibitive cost.